The BLS announced the January inflation report on February 13, indicating that the CPI rose 3.73% in January on a seasonally adjusted annualized basis. This was much larger than December’s increase of 2.83%. As we have mentioned several times, the one month number is extremely volatile and therefore should not necessarily be a sign of trend inflation on the rise. Having said that, our preferred measure of trend inflation also increased slightly from 2.73% to 3.06%.
A large part of the increase came from the shelter component rising over 7% and is about 36% of a household’s expenditures. Energy components fell somewhat. Yet, core CPI inflation rose from 3.35% in December to 4.81% in January (monthly annualized rates). Our measure of trend core CPI inflation also rose, from 3.43% to 3.89%.
The only bright spot to the CPI report is that year-over-year inflation declined. However, as we learned a couple of years ago, this measure is very slow to respond to changes in trend.
What does the CPI report imply for policy? To start, the Fed’s 2% inflation target is for core PCE (personal consumption expenditures) inflation, not (core) CPI inflation. PCE data for January will not be released until February 29. While the year-over-year core PCE inflation rate for January may fall, based on higher trend CPI inflation, it seems likely that trend core PCE inflation will likewise rise. The Fed will probably want to see a steady decline in underlying inflation toward its target before lowering its interest rate. It seems unlikely that the Fed will be lowering rates soon.
The December CPI (Consumer Price Index) report, released by the BLS (Bureau of Labor Statistics) is bad news on the inflation front. By almost any measure, CPI inflation is up. By our recently discussed “constant gain” measure of trend inflation, it rose by 0.4 percentage points for the overall CPI, and by 0.15 percentage points for core CPI (excluding food and energy). On a year-over-year basis, overall CPI rose 0.2 percentage points while core CPI fell by 0.1 points. The figures below show that the one-month annualized inflation rates are also up.
For monetary policy, what presumably matters is not what’s happening with CPI inflation but rather PCE (Personal Consumption Expenditures) price inflation since core PCE inflation is what the Fed looks at. Although it is probably the case that the CPI works to influence the policy makers. The PCE data won’t be released for another two weeks. However, given the broad similarity in the goods covered by the CPI and PCE deflator, it’s a reasonable guess that (core) PCE inflation will also be up. If so, the Fed will be faced with some difficult choices: Do they treat December as (maybe) an aberration and stand pat, or will they view December as the harbinger of another inflationary pulse? Or, cognizant of the long and variable lags associated with the effects of monetary policy, will the Fed leave rates unchanged since they’re already added enough tightening? Having said that, the “trend” line has not risen by much and for the core is basically flat. Therefore, from a long and variable lag perspective it seems doubtful that the Fed will alter their current stance at the meeting at the end of the month.
One of the challenges over the past couple of years has been measuring trend inflation. As shown in the figure below, monthly inflation rates are volatile; 12-month inflation rates are much smoother, but only slowly reflect changes in trend inflation. Previously, we’ve focused on the 3-month inflation rate.
As shown below, the 3-month inflation rate is approximately the average of three 1-month inflation rates. This means that each month, the 3-month inflation rate adds the current 1-month inflation rate, and drops the 1-month inflation rate from 4 months ago. Consequently, the 3-month inflation rate can drop precipitously if the inflation rate being dropped is relatively high.
A different way of putting the issue is that the calculation for the 3-month inflation rate assigns a weight of 1/3 to each of the past 3 months’ inflation rates, and a weight of 0 to inflation rates 4 or more months ago. Why such a discrete change in weights? Why not a more gradual decline in weights?
The remainder of this post gets into the guts of an alternative measure of trend inflation in which the weights on monthly inflation rates decline with their age. Readers uninterested in the details should feel free to jump to the end which presents our new measure of trend inflation.
The 3-month inflation rate as an average of 1-month inflation rates
Consider the calculation of the gross 3-month (non-annualized) inflation rate for November,
where is the price level (for a given month), and the superscript indicates the horizon over which the inflation rate is computed (3 months in this case). The `tilde’ over indicates that the measure of inflation is not annualized. Similarly, 1-month (non-annualized) inflation rates are given by
From the above, it follows that
The gross 3-month inflation rate is the product of the three immediate past 1-month inflation rates. Taking the natural logarithm,
we obtain
where the approximation arises from for close to zero.
If we wish to work with annualized inflation rates, then
Again taking the natural logarithm, we obtain
The 1-month inflation rates will have “12” in the place of “4”. We now have
In other words, the 3-month annualized inflation rate for November is (approximately) the average of the three 1-month annualized inflation rates.
A related problem: computing an average
Given 3 observations on some variable, the sample average or mean is
Now, if we add a fourth observation,
However, computing as above discards the “work” done in calculating . From the calculation of ,
Substituting into the formula for ,
or,
This leads to a well-known formula for recursively computing an average:
where t is the number of observations. It says that the mean at date t is a weighted average of the previous mean, and the current (date t) observation.
This is all well and good if the population average is constant. But what if the population average changes periodically. If we knew when these changes in population average occur, we would simply discard all the old observations, and start computing the average afresh. When we don’t know when changes in the population average occur, an alternative approach is to apply a constant “gain” or weight to new observations:
where is the constant weight.
Application: Trend inflation
The discussion above suggests measuring trend inflation via
In words: trend inflation is a weighted average of the current one-month inflation rate (with weight w), and the previous trend inflation rate (with weight 1-w). Solving this equation backwards gives
That is to say, the measure of trend inflation at t is a weighted average of all past inflation rates, and that the weights decline geometrically with time. Put differently, there is a smooth drop off in the importance attached to previous inflation rates. By way of example, for w=1/3, the weight associated with the current inflation rate is 1/3 = 0.333; with the previous month’s inflation rate, 2/9 = 0.222; with the inflation rate 2 months ago, 4/27 = 0.148; and with inflation 12 months ago, roughly 0.00257 — very small.
Our new measure of trend inflation
The figure below plots our `constant-gain’ measure of trend core PCE inflation for a weight of 1/3 on the latest observation, along with the monthly, 3-month, and annual inflation rates. Relative to the 3-month inflation rate, this measure of trend inflation is somewhat smoother while still responding in a timely fashion to apparent changes in trend inflation.
On November 30, the Bureau of Economic Analysis (BEA) released PCE (Personal Consumption Expenditure) data for October 2023. The BEA notes a small monthly change in the PCE deflator (0.6% at an annual rate, down from 4.5% in September), and that the 12-month PCE inflation rate came in at 3.0% (down from 3.4% in September). These numbers largely mirror the earlier CPI (Consumer Price Index) release: the annualized monthly change fell from 4.8% to 0.5%; the 12-month rate from 3.7% to 3.2%. We prefer to look at the 3-month annualized inflation rate which also fell, from 3.7% to 3.2%; CPI inflation fell from 4.9% to 4.4%.
The cognoscenti know that the Fed’s preferred inflation measure is so-called core PCE inflation (taking out the food and energy components). By this measure, the monthly inflation rate fell from 3.8% to 2.0%, a larger decline than recorded by core CPI (3.9% to 2.8%). The 12-month inflation rate fell by 0.2 percentage points, to 3.5%; core CPI inflation fell by 0.1 percentage point to 3.0%. While our preferred 3-month annualized inflation rate fell, it was essentially unchanged at 2.4%. In contrast, the 3-month annualized change in core CPI rose in October, from 3.1% to 3.4%
In summary, the PCE inflation numbers for October confirm what was seen in the CPI inflation reported about two weeks earlier: inflation is down. How much depends on which series you focus upon. Keeping in mind that CPI inflation tends to run about 0.5 percentage points higher than PCE inflation, the data for October suggest that the US economy is approaching the Fed’s 2.0% inflation target.
Gross Domestic Product (Second Estimate)
On November 29 the BEA announced that real GDP for Q3 was revised up from 4.9% to 5.2%. While revisions to nonresidential fixed investment and state and local government spending were the leading causes of the increase, consumer spending was revised down.
Policy outlook
Given the continued decline in the inflation numbers and the continued strength in the output numbers, it appears the economy has digested the record increases in the Fed Funds rate without roiling the real side of the economy. There seems little doubt at this point that Fed policy is achieving its inflation reduction goal and may have reached the peak of the Fed Funds rate during this cycle. That is, nothing in the data points to the need for further increases in the rate and the market is suggesting some rate declines in 2024.
The BEA announced May PCE (Personal Consumption Expenditure) data that reinforces the earlier CPI (Consumer Price Index) report: Inflation continues to creep down. Annualizing the month-over-month change in the PCE, inflation for May was 1.55%, well below the Fed’s 2% target. As we have commented before, these month-to-month changes contain a lot of noise and our preferred measure is the annualized 3 month change. By this measure, inflation for May was 2.45% – somewhat higher than the 2.2% reported earlier for the CPI. The headline year-over-year PCE inflation rate for May was 3.85%. As we have emphasized in previous posts, this year-over-year measure of inflation is slow to respond to changes in trend which means it will take some time for the year-over-year inflation rates to reflect the lower inflation rates that have come in over recent months.
Less rosy is the inflation picture coming from core PCE (that is, excluding food and energy). While the month-over-month rate was down in May – from 4.65% to 3.84% – the year-over-year and 3 month measures fell by roughly 0.1 percentage points. Presumably, the reason to look at core PCE inflation is that it provides a better gauge of underlying trend inflation than non-core PCE measures. But for our money, the 3 month PCE inflation rate does a good job capturing developments in trend inflation.
For June, expected inflation is now running below 2% at all horizons. Collectively, the results for CPI, PCE and expected inflation suggest that the tightening of monetary policy over the past year-and-a-half has brought down both actual and expected inflation. In this context, the Fed’s decision in June to pause its tightening of monetary policy seems like a good one, especially if one takes into account the well-known long and variable lags of the effects of monetary policy on the economy.
Finally, while we at Economic Snapshot usually do not comment on GDP (Gross Domestic Product) revisions, we are making an exception for the data released on Thursday by the BEA. The output revision was a very large 0.7 percentage points, from 1.27% to 2.00%. This upward revision of output can be attributed to upward revisions in consumption and exports, and a downward revision of imports (which has a positive effect on output since imports are subtracted from output). These effects were partially offset by small revisions in investment and government spending.
Second Revision
Third Revision
Difference
Output
1.27
2.00
+0.73
Consumption
2.65
2.93
+0.28
Investment
-2.10
-2.17
-0.07
Government
0.88
0.85
-0.03
Exports
0.66
1.00
+0.33
Imports
-0.75
-0.37
+0.38
GDP growth for the first quarter of 2023, and contributions to GDP growth by its major components.
The increase in real GDP was widespread according to the state GDP estimates. Real GDP increased in all 50 states in Q1. The largest increase came in North Dakota, 12.4% at annual rate and the lowest in Rhode Island and Alabama at 0.1%. Personal income increased in all but two states, Indiana (-1.0%) and Massachusetts (-0.9%).
The BLS announced that the Consumer Price Index for all urban consumers (CPI-U) rose 0.1% in May on a seasonally adjusted basis. This 0.1% rise translates into an annualized 1.5%, well below the Fed’s 2% inflation target (the grey line in the figure below). Over the last 12 months it rose 4.13%. The preferred measure of Econsnapshot is a measure of inflation based on a 3 month interval. We prefer this measure because the year-over-year number moves very slowly while the month to month number is very volatile as seen in the graph below. This 3 month inflation rate grew at an annual rate of 2.2%, just above the Fed’s 2% target.
The bad news from the CPI report is that core CPI inflation — which strips out the more volatile food and energy prices — continues to run at 5% or more, much higher than the Fed’s target. Indeed, energy prices have declined significantly, down almost 12% year over year. When looking at core CPI over the last month it is the shelter component that was the largest contributor to the rise in prices, accounting for about 60% of the overall increase. One reason to look at core CPI inflation is that it may be a better measure of trend inflation than headline CPI. If so, the Fed still has work to do to bring inflation back to target.
Of course, Fed watchers know that the Fed focuses on inflation as measured by the personal consumption expenditure (PCE) price index. Over long periods of time, PCE and CPI inflation generally move together. That said, on average PCE inflation runs below both the CPI and core CPI. The PCE for May won’t be released until June 30. Consequently, the recent CPI inflation rates may provide useful information regarding the direction for PCE inflation.
Producer Price Index
Hard on the heels of the CPI report came that for the Producer Price Index (PPI). Inflation as measured by the PPI has been trending down since early 2022. Indeed, at an annual rate, the monthly and 3 month inflation rates are negative meaning that the price index has recently been falling.
Roughly speaking, the CPI reflects prices paid by the typical urban household while the PPI captures prices received by domestic producers of goods and services. Since the PPI captures prices received by domestic producers while the CPI measures prices paid by consumers, it’s tempting to conjecture that changes in the PPI will eventually be reflected in the CPI. However, there are differences in coverage which mean that this logic does not necessarily hold. For example, since the PPI measures prices received by US producers, it does not include prices of imports; the CPI does. Also, nearly 1/4 of the CPI includes the imputed rent of owner-occupied housing; this imputed rent is not included in the PPI. Finally, only some of the goods and services covered by the PPI represent purchases by consumers; the remainder are goods and services used by other producers, capital investment, exports and government. The Bureau of Economic Activity says that the PPI for Personal Consumption comes closest to the coverage of the CPI. Yet, the chart below shows that inflation as measured by this last measure is much more volatile than the CPI. The chart also shows that there is no obvious tendency for PPI inflation to lead CPI inflation.
Automotive Prices
Since the onset of the pandemic, much has been said and written about supply chain problems, with the automotive sector receiving particular attention, such as this article that makes several blunders and left out some important economics as well. Anyone who has tried to buy a new car knows that there are very long delivery lags, especially for electric vehicles. These issues in the new car market has spilled over into the used car market where prices have also risen. Keep in mind that a one time increase in the price of, say, new cars is not what we typically mean by `inflation’. To be sure, such a one time increase will, for a time, lead to an increase in measured inflation. However, this effect will dissipate with time. The chart below is based on price indices from the CPI. The used car inflation rate was much higher than that of new cars from mid-2020 to mid-2022. Recently, used car prices have been falling, and new car price inflation is moderating. Automotive maintenance and repair price inflation continues to increase.
Finally, turn again to the difference between the PPI and other price indices. From the PPI, prices received by domestic automotive producers grew rapidly through 2021 and 2022, with an inflation rate as high as 30%. While those prices have started to decline, the price level has risen 28.5% since May 2020. Granted, automotive inflation as measured by either the CPI or PCE price index also rose, but not nearly as much as recorded by the PPI, and the recent decline in PPI automotive prices has translated into a slowing of these prices as measured by the CPI and PCE.
The June 13-14 meeting of the Fed revealed a pause in rate hikes. As the graphs above show, there are certainly signs that the Fed’s early moves have worked in their favor. As we remarked above, given the core CPI numbers there still may be more work to do…and the Fed made it clear in the statement that more rate hikes are likely.
The March CPI (Consumer Price Index) brought decidedly mixed news. Year-over-year, CPI inflation fell from 6% in February to 5% in March. Indeed, the year-over-year inflation rate has trended down since mid-2022. However, as we have pointed out in earlier posts, year-over-year measures of inflation are slow to reflect recent changes in trend since they are 12 month averages of past monthly inflation rates. The good news is that monthly (annualized) inflation is down from 4.5% (February) to 0.6% (March), well below the Fed’s 2% inflation target. A glance at the chart below will remind regular readers that monthly inflation rates exhibit considerable variability. Our preferred measure is the 3-month average of monthly inflation rates. This measure declined more modestly, from 4.1% to 3.8%. More importantly, the 3-month average inflation rate is still well above the Fed’s 2% target.
The news is decidedly worse when looking at core CPI inflation (that is, excluding the volatile food and energy components). On a year-over-year basis, core CPI inflation rose from 5.5% in February to 5.6% in March. On the other hand, the monthly core CPI inflation rate fell from 5.6% to 4.7%. Again, we prefer to look at the 3 month average to gauge the direction of trend inflation. The 3 month average of core CPI inflation fell slightly, from 5.2% to 5.1%. More troubling is that these measures are all well above the Fed’s 2% inflation target.
The producer price index (PPI) was released today that offered up a little more good news. The PPI fell 0.5% in March. Moreover, as noted by the BLS, “two-thirds of the decline in the index for final demand can be attributed to a 1.0-percent decrease in prices for final demand goods. The index for final demand services moved down 0.3 percent.”
Finally, short term inflation expectations have risen: For the one year horizon, from 2.1% in March to 2.6% in April; at the two year horizon, from 2.2% to 2.4%. These developments are, presumably, unwelcome by policymakers who are worried about higher inflation expectations becoming entrenched. Fortunately, the five year expected inflation rate fell from 2.2% to 2.1% while 10 year expectations dropped from 2.3% to 2.1%.
Overall, as mentioned at the outset, the news is mixed. Yes, the CPI is down. But, the year over year core CPI is up. The main reason for the difference between the CPI and CORE CPI is that energy prices fell: gasoline, down 17.4%, and fuel oil, down 14.2%. Given the highly volatile nature of food and energy it is useful to pay attention to the core measure.
Inflation as measured by the Consumer Price Index (CPI) was down, again, in December. The monthly change for the CPI in December came in at -0.079% after increasing 0.096% in November and 0.44% in October. The year over year change in December was 6.42% following 7.12% in November and 7.76% in October. (Since we use seasonally adjusted CPI data, our annual inflation rates differ slightly from the headline numbers that use unadjusted data.) In fact, since July the monthly annualized inflation rate consistently ran below the annual inflation rate, as shown in the figure below. Roughly speaking, the annual inflation rate is the average of the previous 12 months’ inflation rates. As a result, when the monthly inflation rates are below the annual inflation rate — as has been the case in the second half of 2022 — the annual inflation rate will fall. Conversely, when the monthly inflation rate exceeds the annual inflation rate, the annual inflation rate will rise, as it did between July 2020 and June 2022. This discussion implies that it will take another six months of low monthly inflation rates until the annual inflation rate will be reported to be low.
At this stage, it’s helpful to take a step back and ask: What exactly do we mean by “inflation”? In general, inflation refers to an on-going increase in the general level of prices. Operationally, inflation is typically measured by the percentage change in a price index like the CPI, Core CPI (the CPI excluding its more volatile food and energy components), or the Personal Consumption Expenditure (PCE) price index, to name but three. As shown in the next figure, over long horizons, these three measures of inflation tend to move together.
A couple of issues arise. First, over what horizon should inflation be computed? Since inflation is an ongoing process, monthly inflation rates don’t do the trick since they’re far to volatile (see the first chart above). While annual inflation rates are much smoother than their monthly counterparts, annual inflation rates are slow to reflect changes in trend as in the second half of 2022. A simple rule like “Use a three or four month average of the monthly inflation rates” is tempting, but arbitrary. It is, perhaps, best to look at both annual and monthly inflation rates and apply some judgement.
A second issue is that a once-and-for-all increase in the price level is not really “inflation” in the sense of a continuing increase in the price level. However, the (annual) inflation rate as computed from, say, the CPI will record higher inflation following such a one-time change in the price level. Indeed, such a change in the price level will lead to an increase in reported inflation for 12 months. The relevance of this second issue is that the war in Ukraine pushed up global food and energy prices. To the extent that these price increases are permanent, they do not contribute to inflation (on-going increases in prices), although they raise measured inflation. To be sure, core CPI inflation (that is, stripping out the food and energy components) has been lower than overall CPI inflation. Comparing the monthly inflation rates for the CPI and core CPI reveals that monthly core CPI inflation is less volatile. In the event, at least some of the increases in food and energy prices owing to the Ukrainian war have proved to be temporary. Falling food and energy prices in the second half of 2022 have contributed to the decline in monthly CPI inflation. As shown in the chart below, monthly core CPI inflation continues to run well above the Fed’s stated 2% inflation target.
A Quick Primer on Price Level Measurement
The idea of inflation measurement is to uncover a general rise in prices in an economy. The two that garner the most attention, the Consumer Price Index (CPI) and the Personal Consumption Expenditure Index (PCE). The Bureau of Labor Statistics (BLS) calculates the CPI (see the technical note here):
The Consumer Price Index (CPI) measures the change in prices paid by consumers for goods and services. The CPI reflects spending patterns for each of two population groups: all urban consumers and urban wage earners and clerical workers. The all urban consumer group represents about 93 percent of the total U.S. population. It is based on the expenditures
of almost all residents of urban or metropolitan areas, including professionals, the self-employed, the poor, the unemployed, and retired people, as well as urban wage earners and clerical workers.
The CPI is a “cost of living” index as it uses spending patterns of urban consumers:
In calculating the index, price changes for the various items in each location are aggregated using weights, which represent their importance in the spending of the appropriate population group. Local data are then combined to obtain a U.S. city average.
The BLS also reports the “CPI less food and energy,” the CPI-X. The reason for omitting food and energy is that these prices are very volatile and have a large influence on the measure of the CPI because of the larger weights associated with them. For those interested, here are the current weights.
The PCE is calculated by the Bureau of Economic Analysis (BEA) that is also responsible for calculating GDP. According to the BEA:
BEA’s closely followed personal consumption expenditures price index, or PCE price index, is a narrower measure. It looks at the changing prices of goods and services purchased by consumers in the United States. It’s similar to the Bureau of Labor Statistics’ consumer price index for urban consumers. The two indexes, which have their own purposes and uses, are constructed differently, resulting in different inflation rates.
The PCE price index is known for capturing inflation (or deflation) across a wide range of consumer expenses and for reflecting changes in consumer behavior. For example, if the price of beef rises, shoppers may buy less beef and more chicken. Also, BEA revises previously published PCE data to reflect updated information or new methodology, providing consistency across decades of data that’s valuable for researchers. The PCE price index is used primarily for macroeconomic analysis and forecasting.
These are not the only two, however. The Cleveland Fed produces the median CPI and the 16% trimmed mean. Recall that the main idea is to capture a general rise in prices. Removing highly volatile changes, or outliers, better reflects this general rise. Note that the median measure has been stuck at 7% for the last three months.
is the price level (for a given month), and the superscript indicates the horizon over which the inflation rate is computed (3 months in this case). The `tilde’ over 
indicates that the measure of inflation is not annualized. Similarly, 1-month (non-annualized) inflation rates are given by
for 
close to zero.
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as above discards the “work” done in calculating 
. From the calculation of 
,
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is the constant weight.
